DataTable or DataGridView to CSV or HTML file using Clipboard

It turns out that DataGridView.GetClipboardContent() returns all the selected cells of a DataGridView as a type DataObject, which is conveniently consumed by the Windows.Forms.Clipboard class, as well as other WYSIWYG editors from Microsoft. From this you can set the Clipboard, then get the clipboard various data formats, including:
- Comma separated value
- Tab separated value
- HTML

So instead of looping though columns and then rows, you can output the entire DataGridView as a CSV file in just 3 lines of code! (4 if you count setting the ClipboardCopyMode, which can be set in the Form Builder.

Here is the code:

void DataGridViewToCSV(string Filename)
{
   bool allowAddRows = dataGridView1.AllowUserToAddRows;
   bool rowHeadersVisible = dataGridView1.RowHeadersVisible;
   dataGridView1.AllowUserToAddRows = false;
   dataGridView1.RowHeadersVisible = false;

   // Choose whether to write header. You will want to do this for a CSV file.
   dataGridView1.ClipboardCopyMode = DataGridViewClipboardCopyMode.EnableAlwaysIncludeHeaderText;
   // Select the cells we want to serialize.
   dataGridView1.SelectAll(); // One could also use DataGridView.Rows[RowIndex].Selected = true;

   // Save the current state of the clipboard so we can restore it after we are done
   IDataObject objectSave = Clipboard.GetDataObject();
   // Copy (set clipboard)
   Clipboard.SetDataObject(dataGridView1.GetClipboardContent());
   // Paste (get the clipboard and serialize it to a file)
   File.WriteAllText(Filename,Clipboard.GetText(TextDataFormat.CommaSeparatedValue));
   // Restore the current state of the clipboard so the effect is seamless
   if(objectSave != null)
   {
      Clipboard.SetDataObject(objectSave);
   }
   dataGridView1.AllowUserToAddRows = allowAddRows;
   dataGridView1.RowHeadersVisible = rowHeadersVisible;
}

Some improvements

For a tab-delimited file, use the TextDataFormat.Text enum in your call to Clipboard.GetText(). You can also output your DataGridView as HTML by using TextDataFormat.Html instead of TextDataFormat.CommaSeparatedValue, but there is extra header data you have to parse out:

   string result = Clipboard.GetText(TextDataFormat.CommaSeparatedValue);
   result = result.Substring( result.IndexOf("") );

Notes:
- An object must be serializable for it to be put on the Clipboard.